Question

An automobile emissions testing center has six inspectors and tests 50 vehicles per hour. Each inspector can inspect 12 vehicles per hour. How many inspectors would the center require to have a target utilization of 90 percent?

Answer 1

Answer:

The center require to have a 4.6 inspectors, but this on you decide if you have 4 or 5 inspectors, it may not have 4.6 people working.

So then if you decide to have 5 people their utilization percentage is 83.3%, but if you decide to have 4 people their utilization rate will be 104.17% at the risk of defaulting on demand.

Step-by-step explanation:

1. Define your variables

Demand rate= 50 vehicles per hour

Service rate = 12 vehicles per hour per inspector

Inspectors= a

2. Use the formule of the center´s utilization

U= $\frac{Demand}{(Service) X a}$

0,9= $\frac{50}{(12) X a }$

0,9a=$\frac{50}{12}$

a=$\frac{50}{12X0,9}$

a= 4.6

3. According to the center´s utilization formula the center require 4,6 inspectors, but approaches 5 because people cannot be divided. With this numbers of inspectors the utilization is:

U= $\frac{Demand}{(Service) X (No. inspectors)}$

U= $\frac{50}{(12) X (5)}$

U= 83,3%

4. Other option that you will be used is that the center require 4 inspectors. With this numbers of inspectors the utilization is:

U= $\frac{Demand}{(Service) X (No. inspectors)}$

U= $\frac{50}{(12) X (4)}$

U= 104,17%